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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JESTPE.2019.2941583, IEEE Journalof Emerging and Selected Topics in Power Electronics

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Abstract—For the high-power Li-Ion battery (LIB)

Formation and Grading System using multi-stage conversion

structure, bidirectional isolated DC-DC converter with high input

voltage and large output current is needed to achieve isolation and

relatively fixed voltage conversion gain. This paper proposes a

modulation strategy and modifies the topology to achieve

naturally bidirectional power transfer, automatic power sharing

and power limitation for an Input-series-output-parallel (ISOP)

LLC-DCX converter. Firstly, an active Pulse Width Modulation

(PWM) strategy is proposed to avoid synchronous rectifier (SR)

sensing and to achieve the nature bidirectional power flow for

each sub-module. The resonant current always keeps

discontinuous, and the conversion gain can keep constant if

ignoring the conduction resistance. Secondly, clamping diodes are

added in the conventional LLC converter to limit the inrush

current during start-up, and to achieve constant power limitation

under over load condition. Thirdly, with the proposed modulation,

the power sharing of two-module ISOP LLC converter is analyzed

and compared with the conventional ISOP LLC converter.

Finally, experiments based on an 8kW (output:15V/533A)

prototype composed of two-module ISOP LLC converter are

conducted to verify the effectiveness of the proposed solution.

Index Terms—bidirectional isolated DC-DC converter,

nature bidirectional power flow, constant power limitation,

constant voltage gain

I. INTRODUCTION

URING recent years, Li-Ion battery (LIB) is growing in

popularity for battery electric vehicles, portable

electronics, aerospace applications, etc.[1]. The last process for

Manuscript received May 28, 2019; revised August 7, 2019; accepted

August 31, 2019.

This work was supported in part by the National Key R&D Program of

China under Grant 2018YFB0606005, in part by the Key Technology R&D

Program of Hunan Province of China under Grant 2018SK2140, in part by the

National Natural Science Foundation of China under Grant 51907206, in part

by the National Natural Science Foundation of China under Grant 61573384, in

part by the Major Project of Changzhutan Self-dependent Innovation

Demonstration Area under Grant 2018XK2002, and in part by the Fundamental

Research Funds in the Central South University under Grant 2018zzts521.

(Corresponding author: Guo Xu).

The authors are with the Hunan Provincial Key Laboratory of Power

Electronics Equipment and Gird, School of Automation, Central South

University, Changsha 410083, China. (email: [email protected];

[email protected]; [email protected]; [email protected];

[email protected]; [email protected]; [email protected];

[email protected]; [email protected]).

LIB production is to grade battery capacity and performance [2]

by a LIB Formation and Grading System with bidirectional

power capability[3][4]. In view of topology structure, the

system generally consists of three conversion stages including

the AC-DC rectifier, isolated bidirectional DC-DC converter

with relatively fixed conversion gain (DCX) [5][6] and a

bidirectional synchronous buck converter to control

charging/discharging power as illustrate in Fig.1. The AC

rectifier voltage is firstly step-down to a relatively fixed voltage

(around 15V), and then followed with a synchronous

bidirectional buck converter. This two-stages structure is used

to achieve high conversion efficiency and flexible output power

control under wide conversion gain range, as also studied in

[7]-[10].

PWM

Rectifier

AC/DC

Isolated

Bidirectional

DC/DC

LLC-DCX

Grid DC Bus

15V

Synchronous

Bidirectional

Buck Converter

DC/DC

Battery

0-5V

AC/DC LLC-DCX DC/DC

AC/DC LLC-DCX DC/DC

Figure 1. The LIB Formation and Grading System.

For isolated bidirectional DC-DC conversion stage shown in

Fig.1, LLC converter is a suitable topology because of its

soft-switching characteristics for all power devices from zero to

full load range [11][12]. To achieve high conversion efficiency,

Synchronous rectifier (SR) is generally employed for based on

detecting the current zero crossing point or sensing the device

voltage drop [13][14]. These SR technologies are widely used

for LLC converter in unidirectional power applications. While,

if it is used in bidirectional power applications, due to the

asymmetry of both the topology and gain characteristics, SR

must exchange between the two side bridges according to the

power direction. As a result, detecting the power direction and

shifting control logic will both make the control strategy more

complex [15].

In bidirectional power applications, two issues need to be

studied for LLC converter. One is the asymmetry issue for both

control strategy and topology. The other one is the soft-start and

current protection. A symmetrical bidirectional CLLC resonant

converter with two resonant tanks was proposed in [16]-[19].

The voltage gain in forward operation mode is the same as that

A Natural Bidirectional Input-Series-Output-Parallel

LLC-DCX Converter with Automatic Power Sharing

and Power Limitation Capability for Li-Ion Battery

Formation and Grading System Xiaoying Chen, Student Member, IEEE, Guo Xu, Member, IEEE, Shiming Xie, Student Member, IEEE,

Hua Han, Mei Su, Yao Sun, Member, IEEE, Hui Wang, Yonglu Liu, Member, IEEE and Wenjing Xiong

D



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in backward mode. However, it needs to change the control

logic to achieve bidirectional power flow. In [20], researchers

proposed an LLC-LC type bidirectional control strategy for an

LLC-LC type resonant converter. It can achieve bidirectional

power flow automatically without power flow detection.

However, the circulating current of the resonant tank is

increased which decreases the efficiency of LLC converter in

backward mode. In another point of view, adding an auxiliary

inductor can also construct a symmetrical structure which was

proposed in [21]. It can automatically change the power flow

direction by regulating the switching frequency. However, it is

a challenge to transfer power smoothly between different

operating modes. In [22], a bidirectional CLTC resonant

converter was proposed which adds an auxiliary transformer

and an extra resonant capacitor. For these resonant converters,

the efficiency and reliability may be reduced as auxiliary

devices are added.

To achieve soft start and current protection, some methods

were proposed in [23]-[25]. An over-current protection circuit

was proposed that it used the output voltage of the LLC

converter to clamp the voltage of resonant capacitor through an

extra transformer in [23]. An offline calculation method to limit

start-up current was proposed in [24]. However, when the

parameters of resonant tank are changed because of aging or

manufactory mismatching, the theoretical analysis may not be

that accurate. In [25], optimal trajectory control (OTC) was

used to solve the soft start-up and the short-circuit protection,

but this method needs many calculations. The clamping diodes

are added to the secondary side switching network to deal with

the current protecting issue in [26]. When overload condition is

triggered, the resonant converter will operate in DAB-MIXED

mode, and an extra controller is needed to employ to decrease

the duty cycle and to limit the peak value of the resonant

current.

In addition, for high power (>6.6kW) LIB Formation and

Grading System using LLC converter as the isolation stage, the

input voltage is relatively high (650V-750V DC bus voltage

with 380V three phase AC input), and the output current is

large (above 440A, 15V output). To decrease the stress of

power devices, modular structure can be adopted. In ideal case,

when all the parameters are the same, each sub-module can

work at the resonant frequency to achieve stable DCX

operation. While, in non-ideal case, to achieve accurate input

voltage sharing (IVS) and output current sharing (OCS),

frequency modulation control [27]-[29] for the

Input-Series-Output-Parallel (ISOP) LLC resonant converter

will be needed. These frequency modulation strategies are

variable frequency control, and it will cause the operating point

to go away from the optimum resonating point. In addition,

because the gain changes nonlinearly with the frequency, it is

hard to analyze the control mechanism during the transient.

In order to achieve natural bidirectional power flow for

LLC-DCX converter used in LIB Formation and Grading

System, an ISOP LLC converter topology with automatic

power sharing and power limitation capability is studied, which

has the following advantages:

(1) An active Pulse Width Modulation (PWM) modulation

strategy is proposed to avoid SR sensing and to achieve the

nature bidirectional power flow. The resonant current always

keeps discontinuous, which could achieve constant output

voltage gain regardless of the load.

(2) Clamping diodes are added in the LLC converter to limit

inrush current when the converter starts up, and to achieve

constant power limitation during over load operation, which

can improve the system reliability.

(3) To decrease the power rating of single power switch,

ISOP configuration is employed and multi-transformer

structure is adopted for each sub-module. Because the proposed

modulation can achieve constant voltage gain of each

sub-module, the power sharing control can be automatically

achieved.

In this paper, a modulation strategy is proposed to achieve

natural bidirectional power flow for ISOP LLC converters with

automatic power sharing and power limitation capability. The

operation principle analysis of the multi-transformer LLC

converter under the proposed modulation is given in Section Ⅱ.

In Section Ⅲ, the analysis about zero-voltage-switching (ZVS)

condition, the constant voltage gain and the power limitation of

the modified LLC converter under the proposed modulation are

presented. With the proposed modulation strategy, the

automatic power sharing for ISOP structure is analyzed in

Section Ⅳ. The design considerations are given in Section Ⅴ.

The experimental results are shown in Section Ⅵ to verify the

effectiveness of the proposed solution.

Vin

Vin1

Vin2

Iin

Vo

Iout1

Iout2

1#LLC

2#LLC

AC/DC

ISOP System

(a)

Vo

isC

DT

S3a

isC

DT

S1

S2

Lr

ir

A

B

C1

C2

Vin1

D1

D2

Lm

Lm

n : 1

n : 1

S4a S6a

S5a

S3b

S4b

S5b

S6b

(b)

Figure 2. The topology of the LLC resonant converter.

(a)The ISOP structure of the LLC converter.

(b) The individual module (module 1).



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II. THE MODIFIED LLC RESONANT CONVERTER WITH ISOP

STRUCTURE

The structure of ISOP LLC resonant converter is illustrated

in Fig.2(a). There are two sub-modules, and each module is a

multi-transformer LLC converter with two clamping diodes

which is shown in Fig.2(b). Vin is the total input voltage for the

ISOP system, and Vo is the output voltage.

As Fig.2(b) shows, two spilt-capacitors C1, C2, two clamping

diodes D1, D2 and the resonant inductor Lr build up the resonant

tank. Lm is the magnetizing inductor of the isolated transformer

with turns ratio n.

The frequency of the resonant tank fr is shown as

1 2

1

2 ( )r

r

fL C C

=+

(1)

To achieve symmetrical operation of the multi-transformer

rectifier in the secondary side, as shown in Fig.2(b), S3a is

turned on/off synchronously with S3b which is the same for S6a

and S6b. S4a is turned on/off synchronously with S4b which is the

same for S5a and S5b. In practice, the parameters of each

transformer are designed to be the same. Hence, when

analyzing the working modes of the converter under proposed

PWM modulation strategy, the topology shown in Fig.2(b) can

be equivalently represented by the topology shown in Fig.3.

S1

S2

Lr2Lm

ir

iLmA

B

C1

C2

Vin1

D1

D2

Vo

isC

DT

S3

S4

S5

S6

2n : 1

iin iout

Figure 3. The equivalent half-full bridge LLC resonant converter.

Unlike the conventional LLC converter that operating at a

fixed frequency to get a fixed voltage gain, the modified

modulation strategy can achieve fixed voltage gain as long as

the current is discontinuous under fr > fs, where fs is the

switching frequency. The reason of this phenomenon will be

further explained in Section Ⅲ. In the proposed modulation, the

driving signals of S1, S3 and S6 are the same which is different

with that in conventional LLC converter. Identically, the

driving signals of S2, S4 and S5 are the same. And the turn-on

time of the driving signals is controlled to be half of the

resonant period. In addition, there is no SR issue because all

PWM signals are generated actively.

There are four working modes under the proposed

modulation. When LIB Formation and Grading Equipment

works normally, it operates in Mode 1 and Mode 3 which

charges/discharges LIB respectively. When overload occurs,

Mode 1 will change to Mode 2 and Mode 3 will change to

Mode 4, which can automatically achieve power limitation.

A. Mode 1: Forward Power Transmission Mode

During the forward power transmission mode, the energy is

transferred from the primary side to the secondary side of the

transformer. Fig.4 shows the working stages for this mode and

the key waveforms of the converter under this mode are shown

in Fig.5.

S1

S2

Lr2Lm

ir

iLmA

B

C1

C2

Vin1

D1

D2

Vo

isC

DT

S3

S4

S5

S6

2n : 1

(a)

S1

S2

Lr2Lm

ir

iLmA

B

C1

C2

Vin1

D1

D2

Vo

isC

DT

S3

S4

S5

S6

2n : 1

(b)

S1

S2

Lr2Lm

ir

iLmA

B

C1

C2

Vin1

D1

D2

Vo

isC

DT

S3

S4

S5

S6

2n : 1

(c)

S1

S2

Lr2Lm

ir

iLmA

B

C1

C2

Vin1

D1

D2

Vo

isC

DT

S3

S4

S5

S6

2n : 1

(d)

Figure 4. The operation of the converter in forward power transmission

mode.

(a)Stage 1(t0-t1). (b) Stage 2(t1-t2).

(c)Stage 3(t2-t3). (d)Stage 4(t3-t4).

ir

iLm

is

Uds1

Uds2

Uds4

Uds3

S1&S3&S6 S1&S3&S6S2&S4&S5

t1t0 t2 t3 t4 Figure 5. The key waveforms of the proposed converter in forward power

transmission mode.

Stage 1 (t0-t1) [Fig.4(a)]: Before t0, S1 and S2 are turned off.

And the voltages of the junction capacitors of S3 and S6 have

been decreased from Vo to zero. The parasitic anti-parallel

diodes of S3 and S6 then conduct, which provides ZVS

condition for S3 and S6. During this mode, S1, S3 and S6 are

turned on, and resonance occurs among C1, C2 and Lr. The

resonant current ir increases sinusoidally in positive direction

from zero which achieves zero-current-switching (ZCS) for S1.

The voltage of Lm is clamped to nVo, and the magnetizing



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current iLm decreases linearly in negative direction until it is

larger than zero. After that, the magnetizing current iLm

increases linearly in positive direction. The secondary current

of transformer equal to 2n(ir – iLm).

Stage 2 (t1-t2) [Fig.4(b)]: At t = t1, when the resonant current

ir decreases to zero, S1, S3 and S6 are turned off. After that, the

junction capacitors of S1 and S2 resonate with Lr. At the same

time, the voltages across the junction capacitors of S3 and S6

increase to Vo, and the anti-parallel diodes of S4 and S5 are

conducted. Afterwards, the voltage of Lm is inversed, and the

magnetizing current iLm is decreased linearly in positive

direction. The secondary current of transformer is is changed to

be negative.

Stage 3 (t2-t3) [Fig.4(c)]: After t = t2, the resonant inductor

Lr and the junction capacitors of S1 and S2 keep on resonating,

because the voltage across Lm is clamped to nVo. The current of

magnetizing inductor decreases in positive direction, but its

value is always larger than zero which guarantees the

anti-parallel diodes of S4 and S5 to keep on conducting.

Stage 4 (t3-t4) [Fig.4(d)]: Before t = t3, the anti-parallel

diodes of S4 and S5 are conducting which ensures ZVS turn-on

for S4 and S5. At t = t3, S2, S4 and S5 turn on, the current of

resonant inductor increases sinusoidally in negative direction

which is similar to Stage 1.

B. Mode 2: Forward Power Limitation Mode

When charging current of LIB is greater than that in rated

condition, Mode 1 will change to this mode. In overload

situation, both the current of Lr and the voltage across C1 or C2

increase. Once VC1 or VC2 reaches Vin1, D2 or D1 starts

conducting. Then C1 and C2 will be bypassed. Therefore, the

resonance among C1, C2 and Lr will be stopped. When D1 or D2

conducts, the energy transfer will be interrupted from primary

side to the secondary side of the transformer which means that

the power limitation occurs. Moreover, the resonant current ir

will be limited which protects the switching networks and the

resonant capacitors. Fig.6 demonstrates the working stages and


in Fig.7.

S1

S2

Lr2Lm

ir

iLmA

B

C1

C2

Vin1

D1

D2

Vo

isC

DT

S3

S4

S5

S6

2n : 1

(a)

S1

S2

Lr2Lm

ir

iLmA

B

C1

C2

Vin1

D1

D2

Vo

isC

DT

S3

S4

S5

S6

2n : 1

(b)

S1

S2

Lr2Lm

ir

iLmA

B

C1

C2

Vin1

D1

D2

Vo

isC

DT

S3

S4

S5

S6

2n : 1

(c)

Figure 6. The operation of the converter in forward power limitation mode.

(a)Stage 2(t1-t2). (b) Stage 3(t2-t3). (c)Stage 4(t3-t4).

S1&S3&S6 S1&S3&S6S2&S4&S5

Uds1

Uds2

Uds4

Uds3

Uc1

Uc2

iD1

iD2

is

ir

iLm

t1t0 t2 t3t4 t5 Figure 7. The key waveforms of the proposed converter in forward power

limitation mode. Stage 1 (t0-t1) [Fig.4(a)]: This stage is the same as that in

Mode 1.

Stage 2 (t1-t2) [Fig.6(a)]: Before t = t1, Lr resonates with C1

and C2, and the voltage across C2 increases sinusoidally. After

that, VC2 reaches Vin1, and D1 are conducted which causes the

voltage across resonant inductor to change to - nVo. After t = t1,

the current of Lr decreases linearly in positive direction. The

resonance tank stops work, and there is no energy transmitting

to the secondary side of the transformer.

Stage 3 (t2-t3) [Fig.6(b)]: At t = t2, S1, S3 and S6 are turned off.

And the anti-parallel diodes of S2, S4 and S5 conduct after the

voltages of their junction capacitors decrease to zero. The

voltage across resonant inductor Lr then changes to -(Vin1+nVo)

which speeds up the reduction for the current of Lr till it

decreases to zero.

Stage 4 (t3-t4) [Fig.6(c)]: After the current of Lr decreases to

zero, the junction capacitors of S1 and S2 begin to resonant with

Lr. The anti-parallel diodes of S4 and S5 keep on conducting

because is is larger than zero.

Stage 5 (t4-t5) [Fig.4(d)]: This stage is the same as that in

Mode 1.

C. Mode 3: Reverse Power Transmission Mode

For LIB Formation and Grading System, when LIB is

discharged, the energy of LLC converter will be transmitted

from the secondary side to the primary side of transformer,

which is in contrary to the forward transmission mode. Fig. 8

shows the working stages, and the key waveforms of the

converter under this mode are shown in Fig. 9.



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S1

S2

Lr2Lm

ir

iLmA

B

C1

C2

Vin1

D1

D2

Vo

isC

DT

S3

S4

S5

S6

2n : 1

(a)

S1

S2

Lr2Lm

ir

iLmA

B

C1

C2

Vin1

D1

D2

Vo

isC

DT

S3

S4

S5

S6

2n : 1

(b)

S1

S2

Lr2Lm

ir

iLmA

B

C1

C2

Vin1

D1

D2

Vo

isC

DT

S3

S4

S5

S6

2n : 1

(c)

S1

S2

Lr2Lm

ir

iLmA

B

C1

C2

Vin1

D1

D2

Vo

isC

DT

S3

S4

S5

S6

2n : 1

(d)

Figure 8. The operation of the converter in reverse power transmission

mode.

(a)Stage 1(t0-t1). (b) Stage 2(t1-t2).

(c)Stage 3(t2-t3). (d)Stage 4(t3-t4).

ir

iLm

is

Uds1

Uds2

Uds4

Uds3

S1&S3&S6 S1&S3&S6S2&S4&S5

t1t0 t2 t3 t4 Figure 9. The key waveforms of the proposed converter during reverse

power transmission mode.

Stage 1 (t0-t1) [Fig.8(a)]: Before this mode, S1, S3 and S6 are

turned off. And the anti-parallel diode of S1 has been conducted

because the voltage across the junction capacitor of S1 is

decreased to zero which provides the condition for S1 to achieve

ZVS. At t = t0, S1, S3 and S6 are turned on, the resonance occurs

among C1, C2 and Lr. The resonant current ir increases

sinusoidally in negative direction from zero which means S3

and S6 are turned on with ZCS. And the magnetizing current iLm

decreases linearly in negative direction until it changes to zero

for the voltage across the magnetizing inductor Lm is nVo. The

magnetizing current will increase in positive direction after it

changes to zero. This mode ends when the secondary current is

is decreased to zero.

Stage 2 (t1-t2) [Fig.8(b)]: At t = t1, S1, S3 and S6 are turned off.

After that, the junction capacitors of S3, S4, S5 and S6 resonate

with Lr, and the voltage across the junction capacitor of S2

decreases to zero. Then, the anti-parallel diode is conducted.

Afterwards, the voltage across Lm is inversed, and the

magnetizing current iLm is decreased linearly in positive

direction.

Stage 3 (t2-t3) [Fig.8(c)]: After t = t2, the resonant inductor Lr

and the junction capacitors of S3 S4 S5 and S6 keep on resonating

for the voltage across Lm is clamped to nVo. The current of

magnetizing inductor decreases in positive direction, but its

value is always larger than zero which guarantees the

anti-parallel diodes of S2 to keep on conducting.

Stage 4 (t3-t4) [Fig.8(d)]: Before t = t3, the anti-parallel diode

of S2 is conducting which ensures ZVS turn-on for S2. At t = t3,

S2, S4 and S5 are turned on, the current of resonant inductor

increases sinusoidally in positive direction which is similar to

Stage 1.

D. Mode 4: Reverse Power Limitation Mode

When discharging current is higher enough, Mode 3 will

change to this mode. The voltage of C1 or C2 will reach Vin1 if

the current of Lr is high enough. This will cause the conduction

of D1 or D2, and stop the resonance in the resonant tank.

S1

S2

Lr2Lm

ir

iLmA

B

C1

C2

Vin1

D1

D2

Vo

isC

DT

S3

S4

S5

S6

2n : 1

(a)

S1

S2

Lr2Lm

ir

iLmA

B

C1

C2

Vin1

D1

D2

Vo

isC

DT

S3

S4

S5

S6

2n : 1

(b)

S1

S2

Lr2Lm

ir

iLmA

B

C1

C2

Vin1

D1

D2

Vo

isC

DT

S3

S4

S5

S6

2n : 1

(c)

Figure 10. The operation of the converter in reverse power limitation mode.

(a)Stage 2(t1-t2). (b) Stage 2(t2-t3). (c)Stage 3(t3-t4).



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S1&S3&S6 S1&S3&S6S2&S4&S5

Uds1

Uds2

Uds4

Uds3

Uc1

Uc2

iD1

iD2

is

ir

iLm

t1t0 t2 t3 t4 t5 Figure 11. The key waveforms of the proposed converter during reverse

power limitation mode. Fig.10 demonstrates the working stages for this mode, and


in Fig.11.

Stage 1 (t0-t1) [Fig.8(a)]: This stage is the same as that in

Mode 3.

Stage 2 (t1-t2) [Fig.10(a)]: At t = t1, the voltage across C1

reaches to Vin1, and D2 then conducts which stops the resonance.

The voltage across the resonant inductor Lr changes to Vin1-nVo,

and the current of Lr decreases linearly in negative direction.

The energy keeps on transmitting from the secondary side of

transformer to the primary side.

Stage 3 (t2-t3) [Fig. 10(b)]: This stage begins when S1, S3 and

S6 are turned off. After that, the junction capacitors of S3 and S6

are discharged by is until the voltages across S4 and S5 decrease

to zero. The anti-parallel diodes of S4 and S5 then conduct

which changes the voltage across the magnetizing inductor.

Then the current of the magnetizing inductor Lm decreases

linearly in positive direction. The voltage across the resonant

inductor Lr changes to Vin1+nVo which causes ir to decrease

rapidly to zero.

Stage 4 (t3-t4) [Fig. 10(c)]: At t = t3, ir changes to zero which

is shown as Fig. 11. Then resonance occurs among Lr and the

junction capacitors of S1 and S2. The voltage across S2 decreases

to zero, and the anti-parallel diode of S2 then conducts. After

that, Lr resonates with the junction capacitors of S3, S4, S5 and

S6.

Stage 5 (t4-t5) [ see Fig.8(d)]: This stage is the same as that in

Mode 3.

III. ANALYSIS OF THE MODIFIED CONVERTER UNDER THE

PROPOSED MODULATION

A. Constant Voltage Gain under the Proposed Modulation

iout

iin

S1 ON S2 ON S1 ON

Figure 12. The current waveforms of input and output current for the

converter under the proposed modulation.

As Fig.12 shows, iout(t) is equal to |2n[ir(t) – iLm(t)]|, the

average value of iout(t) is written by

3 1

1

1 1

22 ( ) ( )

t t

out r Lm

s t

i n i t t i t t dtT

−

= − − − (2)

Where iin(t) is the input current of the primary side switching

network, and iout(t) is the output current of the secondary side

switching network which is shown in Fig.3. The average value

of iLm is zero. Hence, the average value of iout(t) can be

simplified as

3 1

1

1

4( ) 4

t t

out r in

s t

ni i t t dt n i

T

− = − =

(3)

The input power and output power should keep balance if

ignoring the losses, so the voltage gain can be expressed by

1

1

4

o in

in out

V iM

V i n= = = (4)

From the analysis above, it is concluded that the voltage gain

keeps a constant value as long as power limitation condition is

not trigged. In practice, the conduction resistance and the line

impedance could not be neglected, which causes voltage drop

of the converter, affecting the voltage gain. Thus, the output

voltage considering the conduction resistances can be

calculated as

1

2 2

1 _ _ _ _

+8

16 ( 2 )

8

ino

in o p copper p ds L s copper s ds

VV

n

V P R R n R R R

n

=

− + + + +

(5)

where Rp_copper is the copper resistance of the transformer

primary side. Rp_ds is the conduction resistance of the primary

side switches. Rs_copper is the copper resistance of the

transformer secondary side. RL is the line impedance in output

side of the converter. Rs_ds is the conduction resistance of the

secondary side switches.

B. Power Limitation of the Modified Converter

When the converter works under forward transmission

mode, the transmitted power will be limited if the voltage

across C1 or C2 reaches Vin1. Simultaneously, the clamping

diode of C1 or C2 conducts, which cuts off the path for the

energy to transmit.

At t = t1, the resonant tank stops working, whose key

waveforms are illustrated in Fig. 7. During t0 ~ t1, the

differential equations of the resonant tank can be expressed as

1 2

2

1

( )2 ( )

( )2 ( )

rr in o c

c

r

di tL V nV u t

dt

du tC i t

dt

= − −

=

(6)

Where

1 2 1( ) ( )c c inu t u t V+ = (7)

Based on (6) and (7), ir(t), uc1(t) and uc2(t) can be expressed

as

1 22 (0)( ) (0)cos( ) sin( )in o c

r r

r

V n V ui t i t t

L

− −= + (8)



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1 1

(0)( ) sin( ) (0) 2 cos( )r

c c o o

iu t t u nV t nV

= + − + (9)

2 2 1

1

(0)( ) sin( )+ (0) 2 cos( )

2

r

c c o in

in o

iu t t u nV V t

V nV

= + −

+ −

(10)

Where 1=1/ 2 rC L . ir is increased from zero when the

resonant tank begins to work, so ir(0) is zero. The initial state of

the voltages in this stage are uc1(t) = Vin1 and uc2(t) = 0. This

stage ends when the voltage across C1 decreases to zero and D1

begins to conduct. Therefore, the duration of this stage can be

written by

1 0 1

1

22 2 arccos( )

2

o

r

in o

nVt t t C L

V nV

= − = +

− (11)

The input current of the converter iin(t) can be deduced

1 1 2( ) 2 (0) sin( )in in o ci t C V nV u t = − − (12)

So, the average value of iin(t) is

1 0

1 0

0

1 1 2

0

1 1

2( )

2= 2 (0) sin( )

2=

t t

in in

s

t t

in o c

s

in

s

i i t dtT

C V nV u t dtT

C V

T

−

−

=

− −

(13)

The maximum power transmitted can be deduced by

2

1 1

max 1

2= in

in in

s

C VP i V

T= (14)

From the analysis above, it can be obtained that the clamping

diodes can constantly limit the transmitted power, and the

constant power value is related to the value of C1 and C2. As a

result, the output voltage will be lower than that in normal

operation when overload occurs which can provide automatic

power protection. Fig.13. shows the relationship of the output

voltage and the output current.

Iout

Vo

1

1

Constant Vo Region

Constant Power

Limitation

max o outP V I=

Figure 13. The relationship about the output voltage and the output current.

C. ZVS Condition Analysis

In order to achieve ZVS for switches, the energy of the

resonant inductor should charge/discharge the junction

capacitors completely before the switches are turned on. In the

forward power transmission mode, the switch network of

secondary side can achieve ZVS. As Fig.5 shows, the current of

resonant inductor decreases to zero and is equals to -iLm when S1,

S3 and S6 are turned off. The junction capacitors of S4 and S5 are

discharged by is and the anti-parallel diodes of S4 and S5 then

conduct till S4 and S5 are turned on. is should be large enough to

discharge/charge the junction capacitors, so the magnetizing

current of the transformer should be designed properly to

guarantee ZVS condition for S4 and S5 when they are turned on.

In order to discharge/charge the junction capacitors completely,

the energy stored in magnetizing inductor should be higher than

that in the four junction capacitors.

2 2

_ 3 4 5 6

1 1( )

2 2m Lm peak S S S S oL i C C C C V + + + (15)

Where CS3, CS4, CS5 and CS6 are the junction capacitors of S3,

S4, S5 and S6 respectively. iLm_peak is the peak value of the

magnetizing current which can be expressed as

_4

o

Lm peak

m s

nVi

L f= (16)

is will decrease after S1, S3 and S6 are turned off, but it is

always positive which guarantees ZVS for S2, S4 and S5. So the

current of magnetizing inductor should be larger than zero

during the deadtime.

_ 0o

Lm peak dead

m

nVi T

L− (17)

Where Tdead is the deadtime which can be expresses as

1 1

2 2dead

s r

Tf f

= − (18)

In practice, the same type devices are used for a full bridge,

so the values of CS3, CS4, CS5 and CS6 are assumed the same.

Based on (15) and (16), the range of the magnetizing

inductance can be calculated, which is expressed as

2

364m

s s

nL

f C (19)

Meanwhile, magnetizing current should be larger than zero

during the deadtime, so the duration of Tdead is limited.

According to (17) and(18), it can be deduced that

2 s rf f (20)

In the reverse power transmission mode, the switch network

of primary side can achieve ZVS. the resonant inductor current

equals to iLm, when S1, S3 and S6 are turned off. The junction

capacitors of S1 and S2 are charged/discharged by ir, and then

the anti-parallel diode of S2 conducts. In order to guarantee

ZVS condition of S2, the value of ir should be large enough to

charge/discharge the junction capacitors completely.

2 2

_ 1 2 1

1 1( )

2 2r Lm peak s s inL i C C V + (21)

It is assumed that the values of CS1 and CS2 are the same.

Based on (16) and (21), the range of the magnetizing

inductance is

2 2

1 132

o r

m

s s in

n V LL

C f V (22)

In this mode, the deadtime should also be properly designed

to guarantee ZVS condition, which is the same with that in the

forward power transmission mode.

From analysis above, the range of the magnetizing

inductance is shown as (19) and (22). From (20), it can be seen

that the resonant frequency needs to be lower than twice of the

switching frequency, otherwise, the switches will loss ZVS.



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IV. ANALYSIS OF POWER SHARING FOR ISOP LLC SYSTEM

UNDER THE PROPOSED MODULATION

For high power LIB Formation and Grading System, the

AC/DC stage is a three-phase rectify whose output voltage is

usually controlled between 600V and 750V (380VAC input),

and the output current is large (such as 500A). In order to

reduce the voltage stress for the primary side switching network

and the current stress of the secondary side switching network,

an ISOP structure is used. The schematic block of two-module

ISOP LLC system is shown in Fig.14, where Vin1 and Vin2 are

the input voltage of each LLC module. Iout1 and Iout2 are the

output current of each LLC module. It is assumed that the

efficiency of each LLC converter is 100%, so the input power

of the LLC converter is equal to output power which is shown

as

1 1

2 2

in in out o

in in out o

V I I V

V I I V

=

=

(23)

Vin

Vin1

Vin2

Iin

Vo

Iout1

Iout2

1#LLC

2#LLC

Figure 14. Schematic block of two-module ISOP LLC system.

If the output current balance between each LLC converter are

realized, so

1 2out outI I= (24)

According to (23), in order to achieve the output current

balance, Vin1 and Vin2 should be controlled to keep balance,

namely

1 2in inV V= (25)

It can be known from (24) and (25) that IVS control or OCS

control should be adopted to keep two sub-modules sharing the

same output power. However, for the high output current

application, it does require more effort to sample output current

than input voltage. So, achieving IVS is preferred, which

controls the voltage gain of each LLC converter.

As for the convention LLC converter, a variable-frequency

control is adopted to realize input voltage balance in facing

with parameters mismatching. First Harmonic Approximation

(FHA) is employed to analyze the voltage gain for the LLC

converters. For a single LLC converter, the equivalent model is

shown in Fig.15.

Lr Cr

LmRacVab

Figure 15. The equivalent model for LLC converter.

Rac is the load resistance reflected to primary side of the

transformer, and can be expressed as

2

2

8 o

ac

n RR

= (26)

where Ro is the load resistance. The voltage gain of the LLC

converter is equal to the gain of the resonant tank. The gain of

the LLC converter can be expressed as

2

2 2 2 2 2 2 2

( 1)

( 1) ( 1) ( 1)

f mM

m f f f m Q

−=

− + − − (27)

Where

/,

1,

2

r rs

r ac

r m

r

r r r

L Cff Q

f R

L Lm f

L L C

= =

+ = =

(28)

The output gain curves with different loads are illustrated in

Fig.16. It can be seen from Fig.16 that the variable-frequency

control can be adopted to keep input voltage balance through

adjusting the operating frequency of each LLC converter when

the load is changed or the parameters of two LLC converter are

different.

10 10

Q increaces

1

2

3

Gain

fs / fr Figure 16. Gain characteristics of the convention LLC converter under the

variable-frequency control.

10 10

1

Q increaces

Gain

fs / fr

Constant

Voltage Gain

Region

Figure 17. Gain curves of the LLC converter under proposed modulation.

If the LLC converter operates under the proposed

modulation, the voltage gain of the LLC converter is different

with that in variable-frequency control. Fig.17 shows the

voltage gain curves of the LLC converter under the proposed

modulation. It can be seen from Fig.17 that the voltage gain will

be kept to a constant value if the operating frequency of each

converter is below the resonant frequency. If the parameters of

each sub-module are the same, the voltage gain will be constant

for each sub-module, which can achieve automatic power

sharing. When the parameters are different between two

sub-modules, the voltage gain of two modules will be different

if the duty cycles of the driving signals are the same. In order to

get a fixed voltage gain of two modules, it can change the duty

cycle of the driving signals for each sub-module according to

the resonant period. In the proposed modulation, IVS and OCS

are control by the duty cycle of the driving signals to deal with

parameters mismatching while the operating frequency keeps a



> JESTPE-2019-05-0417 <

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constant value and the working modes for two sub-modules are

the same. As for the convention LLC converter, in order to

achieve IVS and OCS control, the operating frequency of two

sub-modules may be different, which will cause difference in

working condition and ZVS condition between two

sub-modules.

V. DESIGN CONSIDERATION

A. The Turns Ratio of the Transformer

As analyzed in Section Ⅲ, with proposed modulation, the

multi-transformer LLC converter can achieve constant voltage

gain as long as the output power is not higher than the power

limitation value.

The relationship between the voltage gain and the turns ratio

of the transformer was deduce in (4). And the turns ratio of the

transformer is expressed as

8

in

o

Vn

V= (29)

B. Resonant Tank Design

When LLC converter works in power limitation mode, the

voltages across the resonant capacitors are clamped by the

clamping diodes which limits the power. So, the resonant

capacitance determines the maximum output power and it can

be calculated according to the maximum power, which is

shown as

max

1 2

12 s in

PC

f V= (30)

Pmax is the maximum output power of each LLC converter.

And the resonant inductance can be calculated by

2 2

1

1

8r

s

LC f

= (31)

C. Current Stress of The Clamping Diodes

When overload occurs, D1 and D2 will be conducted. As

Fig.7 shows, at t = t1, the voltage of C1 decreases to zero and D1

then conducts. After that, the current of D1 decreases linearly,

because the voltage across Lr changes to -2nVo. After S1 is

turned off, the voltage across Lr changes to -(2nVo+Vin1). So, the

current of D1 can be shown as

1_1 max 1 1 2

1

1_ 2 1 2 2 2 3

2( ),

( )+2

( ) ( ),

o

D D

r

D

in o

D D

r

nVi I t t t t t

Li t

V nVi i t t t t t t

L

= − −

=

= − −

(32)

where IDmax is the current of D1 when t = t1 which is shown as

max ( )D rI i t= (33)

where t is shown in (11). And t2 can be solved by

2 1

1

2 s

t t tf

− = − (34)

At t = t3, the current of D1 decreases to zero, so t3 can be

solved as

max 1

3

2 4

2 4

in s r D s o

s in s o

V f L I t f V nt

f V f V n

+ +=

+ (35)

Then the RMS of iD2(t) can be expressed as (36).

32

1 2

2 2

1_ 1_1 1_ 22 ( )

tt

D RMS s D D

t t

i f i dt i dt= + (36)

To simplify the calculation, magnetizing current is neglected.

Fig.18 shows the comparison between the current of clamping

diode and the current of resonant inductor when the output

power is larger than the rated power where ILr_nom is the RMS

resonant current in the rated condition. It can be seen that the

current of clamping diode is only a small fraction of the

resonant inductor current. Therefore, a very low power rating

diode can be adopted to achieve the power limitation.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 2 3 4 5 61 2 3 4 5 6

1

0.4

1.6

0

Id1_rms /ILr_nom

ILr_rms /ILr_nom

Iout /Iout_max

Norm

ali

zed

Valu

e

Figure 18. The comparison of the resonant current and the clamping diode

current when over load condition.

VI. COMPARISON AND EXPERIMENTAL VERIFICATION

A. Modulation Strategy Comparison

With the proposed modulation, LLC converter achieves

naturally bidirectional power transfer and theoretically keeps a

constant voltage gain. In practice, for the primary side and

secondary side switches, all driving signals whose duty cycle

always keeps constant are the same regardless of the load.

Besides, when the power flow direction is changed, the energy

of resonant tank will be automatically and smoothly transferred.

Under the proposed modulation, PWM modulation of LLC

converter is actively generated, no needing of considering the

power transfer direction and current zero crossing point. In

addition, the output voltage gain can keep constant in ideal

theoretical analysis and changes slightly in practice due to the

effect of conduction resistances.

In [21], a modulation was proposed to achieve automatic

forward and backward mode transition for LLC converter.

0

0.2

0.4

0.6

0.8

1

S1 S2

0

0.2

0.4

0.6

0.8

1

S3 S4

0

-5

-10

5

10

Ir ILm

0.003975 0.00398 0.003985 0.00399 0.003995 0.004

Time (s)

0

-50

-100

50

100

Iss

S1

S2

S3

S4

ir

iLm

is

(a)



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0

0.2

0.4

0.6

0.8

1

S1 S2

0

0.2

0.4

0.6

0.8

1

S3 S4

0

-10

-20

10

20

Ir ILm

0.003975 0.00398 0.003985 0.00399 0.003995 0.004

Time (s)

0

-100

-200

-300

100

200

300

Iss

S1

S2

S3

S4

ir

iLm

is

(b)

Figure 19. The key waveforms of the converter worked under the

modulation proposed in [20].

(a) Forward power transmission mode.

(b) Reverse power transmission mode.

There are six working modes of the converter with different

voltage gain and output current state. In the modulation, all the

MOSFETs in the converter are operated with same frequency,

but the pulse width of gate driving signals for primary side

MOSFETs and secondary side MOSFETs are different

according to the working modes.

In [20], a control strategy was proposed to achieve

bidirectional power flow automatically without power flow

detection. Under the modulation, the key waveforms of the

converter which are simulated by PSIM are illustrated in

Fig.19.

As seen, the pulse width of the driving signals of primary

side switches and secondary side switches always keep

constant whatever the power flow direction is. When the

converter works in backward mode, for the asymmetric driving

signal of primary side switches and secondary side switches,

circulating current will be generated, which leads to high RMS

value of transformer secondary current.

The comparisons for resonant current and transformer

secondary current are show in Fig.20. As seen, when LLC

converter works in forward mode, both the RMS value of the

resonant current and RMS value of transformer secondary

current are almost the same for two kinds of control strategies.

However, when the converter works in reverse mode under the

control strategy proposed in [20], the RMS value of transformer

secondary current is higher than that when the converter works

under the proposed modulation. Consequently, with the

proposed modulation, the circulating current of LLC converter

will be reduced.

RM

S C

urr

en

t(A

)

Forward Mode Transmitted Power(kW)

Is_rms (modulation in [18] )

Is_rms (proposed modulation)

Ir_rms (modulation in [18] )

Ir_rms (proposed modulation)

(a)

Reversed Mode Transmitted Power(kW)

RM

S C

urr

en

t(A

) Is_rms (modulation in [18])

Is_rms (proposed modulation)

Ir_rms (modulation in [18])

Ir_rms (proposed modulation)

(b)

Figure 20. The comparisons for RMS of resonant current and

current of secondary side of transformer.



B. Experimental results

An 8kW experimental prototype composed of two DC-DC

modules using ISOP configuration is built to verify the

effectiveness of the proposed solution. The specifications of

each DC-DC module are given in TABLE Ⅰ. The input voltage

of the converter is 720V, and the output voltage is 15V. The

switching frequency of the converter is 75kHz. The primary

side switches are IPW65R041CFD produced by Infineon

Technologies and the secondary side switches are

PSMN1R5-40PS produced by Nexperia. The clamping diodes

are ES8GC produced by Jingdao Microelectronics. Each switch

on the secondary side is connected in parallel by two

MOSFETs. The experimental prototype is shown in Fig.21.

Figure 21. The experimental prototype.

The steady-state waveforms under the proposed modulation

are shown in Fig.22. Fig.22(a) is the forward transmission

waveforms for the resonant current and the driving signals, and

Fig.22(b) shows the waveforms under the reverse power

transmission mode. It can be seen that the driving signal is the

same for the primary side and the secondary side. And the

resonant current is discontinuous as the resonance starts at

when the driving signals are turned on.

Fig.23. shows the soft-switching waveforms. In the forward

power transmission mode, the switches of the secondary side

can realize ZVS whose waveforms are illustrated in Fig.23(a),



> JESTPE-2019-05-0417 <

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and the switches of the primary side can achieve ZVS in the

reverse power transmission mode whose waveforms are shown

in Fig.23(b).

TABLE Ⅰ

PARAMETERS OF THE EXPERIMENTAL PROTOTYPE

Item Detail

Input Voltage (Vin) 720V

Output Voltage (Vo) 15V

Rated Power (P) 8000W

Turns Ratio (n) 6:1

Resonant Capacitance (C1 & C2) 250nF

Resonant Inductance (Lr) 5.8uH

Magnetizing Inductance (Lm) 125uH

Switching Frequency (fs) 75kHz

Primary side switches IPW65R041CFD

Secondary side switches PSMN1R5-40PS

Clamping Diodes ES8G`C

Vgs1(10V/div)

Vgs3(10V/div)

iLr(20A/div)

Vo(25V/div) t(4μs/div)

(a)

Vgs1(10V/div)

Vgs3(10V/div)

iLr(20A/div)


(b)

Figure 22. Steady-state waveforms under the proposed modulation.



The dynamic waveforms are shown in Fig.24. The

waveforms for exchanging between forward power

transmission mode and reverse power transmission mode are

shown in Fig.24(a) and Fig.24(b), respectively. In Fig.24(a),

the energy is transmitted from primary side to the secondary

side, in which the power flow is changed from 6kW to -6kW,

and Fig.24(b) shows the transition from reverse mode to

forward mode. As seen in Fig.24, the resonant current changes

smoothly when the power flow direction is changed, showing

that the converter can achieve natural bidirectional power flow

under the proposed modulation.

Vgs3(10V/div) Vds3(10V/div)

iLr(20A/div)


ZVS

(a)

iLr(20A/div)

Vgs1(10V/div) Vds1(250V/div)


ZVS

(b)

Figure 23. Soft-switching waveforms under the proposed modulation.



iLr(20A/div)

Vo(25V/div) t(100ms/div)

Forward mode Reverse mode

(a)

iLr(20A/div)


Reverse mode Forward mode

(b)

Figure 24. Dynamic waveforms under the proposed modulation.

(a) Forward power transmission mode to reverse power transmission mode.

(b) Reverse power transmission mode to forward power transmission mode.

Fig.25 shows the dynamic response of the load step-change

for the converter. Fig.25(a) illustrates the response time, which

is 2ms, for the load changes from 3600W (15V, 240A) to

5400W (15V, 360A). The load changes from 3600W (15V,

240A) to 5400W (15V, 360A) is shown in Fig.25(b) and the

response time is 1ms.



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t(2ms/div)

Vin1(250V/div) Vin2(250V/div)

Vin1-Vin2(200V/div)

2ms

3600W 5400W

(a)

t(2ms/div)

Vin1(250V/div) Vin2(250V/div)

Vin1-Vin2(200V/div)iLr(20A/div)

1ms

3600W5400W

(b)

Figure 25. Dynamic response of the load step-change for the converter.

(a)3600W to 5400W. (b)5400W to 3600W.


iLr(20A/div)

Vds1(250V/div)

Figure 26. Soft-start waveforms.

iLr(20A/div)


Uc1(250A/div)

Vo = 15V

(a)

iLr(20A/div)


Uc1(250A/div)

Voltage is

clamped

Vo = 11V

(b)

Figure 27. Power limitation waveforms.

(a) Normal operation mode. (b) Over load operation mode.

The soft-start waveforms are shown in Fig.26. It can be seen

that the current is limited in an acceptable range. The

waveforms in power limiting mode are shown as Fig.27. The

waveforms for the voltage of resonant capacitor and the current

of resonant inductor in normal operation mode are shown in

Fig.27(a). From Fig.27(b), it can be seen that the voltage across

the resonant capacitor is clamped by the clamping diodes and

the output voltage is dropped to achieve constant output power.

The waveforms of IVS and OCS are shown in Fig.28. It can

be seen that the resonant currents of two LLC modules are the

same except the phase-shifted angle for that interleaved PWM

signals are adopted to reduce the output current ripples. And the

input voltages are the same which are shown in Fig.28(a).

When the load is changed, IVS and OCS can also be obtained

with proposed modulation, which are shown in Fig.28(b) and

Fig.28(c) where the input voltages of two modules are almost

the same.

Fig.29 shows the waveforms when resonate parameters of

the two modules are mismatched. The resonant capacitor of

module #1 is 250nF, and the other one is 313nF, which is 25%

larger. Fig.29(a) shows the resonant current and driving signals

for two modules, and Fig.29(b) shows the input voltage sharing

waveforms. As seen, even though the mismatching of

parameters will cause overshoot of resonant current, the

difference of the input voltages (Vin1-Vin2) is still small as shown

in Fig.29(b), indicating that the power sharing can be well

iLr1(20A/div) iLr2(20A/div)

Vin1(250V/div)

Vin2(250V/div)

Vin1-Vin2(200V/div)

(a)

Vin1(250V/div)

Vin2(250V/div)

Vin1-Vin2(200V/div)


(b) Vin1(250V/div)

Vin2(250V/div)

Vin1-Vin2(200V/div)


(c) Figure 28. IVS and OCS waveforms.

(a) Steady waveforms (b) Load changing waveforms.



> JESTPE-2019-05-0417 <

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achieved. Therefore, with the proposed modulation, the two

modules of the converter will keep balance in power even

though the parameters of resonant tank are mismatched in a

controlled tolerance (25%).

Fig.30 shows different results about the output voltage

changing along with the output power. Under the ideal case, the

output voltage will keep a constant value whatever how much

the power is transferred. However, when considering parasitic

resistances whose value are demonstrated in TABLE Ⅱ,

according to (5), the output voltage will drop slightly if the

output power Po increases.

TABLE Ⅱ

THE VALUES OF EACH CONDUCTION RESISTORS

Item Value

Rp_copper 0.12mΩ

Rp_ds 20.5mΩ

Rs_copper 0.13mΩ

RL 0.11mΩ

Rs_ds 1.3mΩ

Ou

tpu

t V

olt

age(V

)

Output Power(kW)

Experiment results

Idea analysis

Consider parasitic

resistance

(0A) (133A) (266A) (400A) (533A)

Figure 30. The output voltage curves with different power.

The difference will be larger as the load increases, mainly

caused by the conduction voltage drop of the power devices.

Although the voltage gain is changed for the conduction

resistance, the load regulation of the converter is acceptable for

LIB Formation and Grading System, because there is another

voltage regulation stage as shown in Fig.1. It can be seen from

the curves that the output voltage is close to that in ideal case

when output power is below 2kW. When the power increases,

the voltage drop will increase slightly, which is within 0.5V.

And the experimental results are close to the results of the

theoretical analysis. The efficiency of the LLC converter is

shown in Figure.31. The maximum efficiency of the LLC

converter is 95% and the full load efficiency is 91%.

Output Power(kW)E

ffic

ien

cy

Figure31. Efficiency of the LLC converter.

VII. CONCLUSION

In this paper, a PWM modulation strategy and modified

topology are studied for achieving naturally bidirectional

power transfer, automatic power sharing and power limitation

capability of an ISOP LLC-DCX converter. Under the

proposed modulation, constant voltage gain is achieved for

each sub-module if ignoring the conduction resistances. The

power sharing of the converter or IVS and OCS for the ISOP

system can be achieved even in the case when the parameters of

the resonant tank are mismatched in a controlled tolerance

between two sub-modules. By adding the clamping diodes, the

start-up current can be limited and constant power limitation is

realized. The working modes of operation, constant voltage

gain characteristics, power sharing and limitation capability are

analyzed in this paper, and the design considerations are given

for the modified LLC converter. The experimental results have

shown that the proposed solution is effective in the aspect of

bidirectional power transfer, power sharing of sub-module, soft

start and dynamic performances, which could be an attractive

option for the high-power LIB Formation and Grading System.

REFERENCES

[1] J. Bae, B. L.H Nguyen, and H. Cha, “A novel battery formation

equipment using two-stage differential buck converter,” in 2016

IEEE Transportation Electrification Conference and Expo,

Asia-Pacific (ITEC Asia-Pacific), 2016, pp. 740-744.

[2] M. Wolter, G. Fauser, C. Bretthauer and M. A. Roscher,

“End-of-line testing and formation process in Li-ion battery

assembly lines,” in International Multi-Conference on Systems,

Signals & Devices, 2012, pp. 1-3.

t(4μs/div)

#1Vgs1(10V/div) #2Vgs1(10V/div)


mismatched

(a)

mismatched

Vin1(250V/div)=366V Vin2(250V/div)=363V

Vin1-Vin2(200V/div)


t(4μs/div)

(b)

Figure 29. The waveforms when the parameters of two resonant tank are

mismatched.

(a) The driving signals and the resonant currents.

(b) The balance in the input voltages of two modules.



> JESTPE-2019-05-0417 <

14

[3] D. Sha, X. Wang and D. Chen, "High-Efficiency Current-Fed

Dual Active Bridge DC–DC Converter with ZVS Achievement

Throughout Full Range of Load Using Optimized Switching

Patterns," IEEE Transactions on Power Electronics, vol. 33, no.

2, pp. 1347-1357, Feb. 2018.

[4] D. Sha, X. Wang, K. Liu and C. Chen, "A Current-Fed

Dual-Active-Bridge DC–DC Converter Using Extended Duty

Cycle Control and Magnetic-Integrated Inductors with

Optimized Voltage Mismatching Control," IEEE Transactions

on Power Electronics, vol. 34, no. 1, pp. 462-473, Jan. 2019

[5] D. Gu, Z. Zhang, Y. Wu, D. Wang, H. Gui, L. Wang, “High

Efficiency LLC DCX Battery Chargers with Sinusoidal Power

Decoupling Control,” in 2016 IEEE Energy Conversion

Congress and Exposition (ECCE), 2016, pp. 1-7.

[6] M. Fu, C. Fei, Y. Yang, Q. Li and F. Lee, "A GaN-Based DC/DC

Module for Railway Applications: Design Consideration and

High-Frequency Digital Control," IEEE Transactions on

Industrial Electronics, Early Access.

[7] W. Feng, P. Mattavelli, F. C. Lee, “Pulse width Locked Loop

(PWLL) for Automatic Resonant Frequency Tracking in LLC

DC–DC Transformer (LLC -DCX),” IEEE Transactions on

Power Electronics, vol. 28, no. 4, pp. 1862-1869, Apr. 2013.

[8] H. Ma, W. Liu, J. Wang, C. Zheng and G. Lu, "Two-stage power

supply based on double resonant tank LLC-DCX for magnetic

levitation control system applications," in 2015 IEEE Applied

Power Electronics Conference and Exposition (APEC),

Charlotte, NC, 2015, pp. 3195-3200.

[9] Ü. Ş. Alemdar and O. Keysan, “Design and implementation of an

unregulated DC-DC transformer (DCX) module using LLC

resonant converter,” in 8th IET International Conference on

Power Electronics, Machines and Drives (PEMD 2016),

Glasgow, 2016, pp. 1-6.

[10] C. Fei, M. H. Ahmed, F. C. Lee and Q. Li, “Two-Stage 48 V-12

V/6 V-1.8 V Voltage Regulator Module with Dynamic Bus

Voltage Control for Light-Load Efficiency Improvement,” IEEE

Transactions on Power Electronics, vol. 32, no. 7, pp.

5628-5636, July 2017.

[11] W. Sun, Y. Xing, H. Wu and J. Ding, "Modified High-Efficiency

LLC Converters with Two Split Resonant Branches for Wide

Input-Voltage Range Applications," IEEE Transactions on

Power Electronics, vol. 33, no. 9, pp. 7867-7879, Sept. 2018.

[12] T. Sun, X. Ren, Q. Chen, Z. Zhang and X. Ruan, “Reliability and

efficiency improvement in LLC resonant converter by adopting

GaN transistor,” in 2015 IEEE Applied Power Electronics

Conference and Exposition (APEC), Charlotte, NC, 2015, pp.

2459-2463.

[13] D. Fu, Y. Liu, F. C. Lee and M. Xu, “A Novel Driving Scheme

for Synchronous Rectifiers in LLC Resonant Converters,” IEEE


1321-1329, May 2009.

[14] X. Wu, G. Hua, J. Zhang and Z. Qian, “A New Current-Driven

Synchronous Rectifier for Series–Parallel Resonant (LLC)

DC–DC Converter,” IEEE Transactions on Industrial

Electronics, vol. 58, no. 1, pp. 289-297, Jan. 2011.

[15] H. Li et al., “A 6.6kW SiC bidirectional on-board charger,” in

2018 IEEE Applied Power Electronics Conference and

Exposition (APEC), San Antonio, TX, 2018, pp. 1171-1178.

[16] W. Chen, P. Rong and Z. Lu, “Snubberless Bidirectional

DC–DC Converter with New CLLC Resonant Tank Featuring

Minimized Switching Loss,” IEEE Transactions on Industrial

Electronics, vol. 57, no. 9, pp. 3075-3086, Sept. 2010.

[17] J. Jung, H. Kim, M. Ryu and J. Baek, “Design Methodology of

Bidirectional CLLC Resonant Converter for High-Frequency

Isolation of DC Distribution Systems,” IEEE Transactions on

Power Electronics, vol. 28, no. 4, pp. 1741-1755, April 2013.

[18] Z. U. Zahid, Z. M. Dalala, R. Chen, B. Chen and J. Lai, “Design

of Bidirectional DC–DC Resonant Converter for

Vehicle-to-Grid (V2G) Applications,” IEEE Transactions on

Transportation Electrification, vol. 1, no. 3, pp. 232-244, Oct.

2015.

[19] P. He and A. Khaligh, “Comprehensive Analyses and

Comparison of 1 kW Isolated DC–DC Converters for

Bidirectional EV Charging Systems,” IEEE Transactions on

Transportation Electrification, vol. 3, no. 1, pp. 147-156, March

2017.

[20] J. Zhang, J. Liu, J. Yang, N. Zhao, Y. Wang and T. Q. Zheng,

“An LLC-LC Type Bidirectional Control Strategy for an LLC

Resonant Converter in Power Electronic Traction Transformer,”

IEEE Transactions on Industrial Electronics, vol. 65, no. 11, pp.

8595-8604, Nov. 2018.

[21] T. Jiang, J. Zhang, X. Wu, K. Sheng and Y. Wang, “A

Bidirectional LLC Resonant Converter with Automatic Forward

and Backward Mode Transition,” IEEE Transactions on Power

Electronics, vol. 30, no. 2, pp. 757-770, Feb. 2015.

[22] C. Wang, S. Zhang, Y. Wang, B. Chen and J. Liu, “A 5-kW

Isolated High Voltage Conversion Ratio Bidirectional CLTC

Resonant DC–DC Converter with Wide Gain Range and High

Efficiency,” IEEE Transactions on Power Electronics, vol. 34,

no. 1, pp. 340-355, Jan. 2019.

[23] X. Xie, J. Zhang, C. Zhao, Z. Zhao and Z. Qian, “Analysis and

Optimization of LLC Resonant Converter with a Novel

Over-Current Protection Circuit,” IEEE Transactions on Power

Electronics, vol. 22, no. 2, pp. 435-443, March 2007.

[24] R. Zheng, B. Liu and S. Duan, “Analysis and Parameter

Optimization of Start-Up Process for LLC Resonant Converter,”

IEEE Transactions on Power Electronics, vol. 30, no. 12, pp.

7113-7122, Dec. 2015.

[25] C. Fei, F. C. Lee and Q. Li, “Digital Implementation of Soft

Start-Up and Short-Circuit Protection for High-Frequency LLC

Converters with Optimal Trajectory Control (OTC),” IEEE


8008-8017, Oct. 2017.

[26] L. Wang, Q. Zhu, W. Yu and A. Q. Huang, “A Medium-Voltage

Medium-Frequency Isolated DC–DC Converter Based on 15-kV

SiC MOSFETs,” IEEE Journal of Emerging and Selected Topics

in Power Electronics, vol. 5, no. 1, pp. 100-109, March 2017.

[27] G. Yang, P. Dubus and D. Sadarnac, “Analysis of the load

sharing characteristics of the series-parallel connected

interleaved LLC resonant converter,” in 2012 13th International

Conference on Optimization of Electrical and Electronic

Equipment (OPTIM), Brasov, 2012, pp. 798-805.

[28] Y. Hayashi, H. Toyoda, T. Ise and A. Masumoto, “Contactless

DC connector based on ISOP-IPOS topology for high power

density 380 V DC power feeding system,” in 2014 16th

European Conference on Power Electronics and Applications,

Lappeenranta, 2014, pp. 1-10.

[29] J. Chen, D. Sha and X. Liao, “Decentralized control strategy for

input-series-output-parallel modular LLC resonant DC/DC

converters,” in 2015 IEEE 2nd International Future Energy

Electronics Conference (IFEEC), Taipei, 2015, pp. 1-5.



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Xiaoying Chen was born in Fujian, China,

in 1995. He received the B.S. degree in

electronic engineering from Central South

University, Changsha, China, in 2017,

where he is currently working toward the

Ph.D. degree. His research interests

include modeling and control of power

electronics converters and high-efficiency

power conversion.

Guo Xu received the B.S. degree in

electrical engineering and automation and

the Ph.D. degree from the Beijing Institute

of Technology, Beijing, China, in 2012

and 2018, respectively. From 2016 to

2017, he was a Visiting Student with the

Center for Power Electronics System,

Virginia Polytechnic Institute and State

University, Blacksburg, VA, USA. Since

2018, he has been with the School of

Information Science and Engineering, Central South University,

Changsha, China, where he is currently an Associate Professor.

His research interests include modeling and control of power

electronics converters, high-efficiency power conversion, and

magnetic integration in power converters.

Shiming Xie was born in Fujian, China, in

1995. He received the B.S. degree in

electronic engineering from Central South


where he is currently working toward the

Ph.D. degree.

His research interests include matrix

converter and DC/DC converters.

Hua Han was born in Hunan, China, in

1970. She received the M.S. and Ph.D.

degrees from the School of Automation,

Central South University, Changsha,

China, in 1998 and 2008, respectively.

She was a Visiting Scholar with the

University of Central Florida, Orlando,

FL, USA, from 2011 to 2012. She is

currently a Professor with the School of

Automation, Central South University.

Her research interests include microgrids, renewable energy

power generation systems, and power electronic equipment.

Mei Su was born in Hunan, China, in

1967. She received the B.S., M.S. and

Ph.D. degrees from the School of

Information Science and Engineering,


China, in 1989, 1992 and 2005,

respectively. Since 2006, she has been a

School of Information Science and Eng

Central South University.

Her research interests include matrix

converter, adjustable speed drives, and wind energy conversion

system.

Yao Sun (M'14) received the B.S., M.S.

and Ph.D. degrees from the School of

Information Science and Engineering,


China, in 2004, 2007 and 2010,

respectively. He is currently with the

School of Information Science and

Engineering, Central South University,

China, as a professor.


converter, micro-grid and wind energy conversion system.

Hui Wang received the B.S., M.S., and

Ph.D. degrees from Central South


2011, and 2014, respectively, where he

has been with the School of Information

Science and Engineering, since 2016.


converters, dc/dc converters, and

solid-state transformer

Yonglu Liu (S’16) was born in

Chongqing, China, in 1989. He received

the B.S., M.S., and Ph.D. degrees in

electrical engineering from Central South


2015, and 2017, respectively, where he

has been an Associate Professor with the

School of Information Science and

Engineering.

His research interests include power

electronics and renewable energy power conversion systems.

Wenjing Xiong was born in Hunan,

China, in 1991. She received the B.S.

degree in automation and the Ph.D. degree

in control science and engineering from


China, in 2012 and 2017, respectively,

where she is currently a Lecturer with the

School of Automation.

Her research interests include matrix

converter and ac/dc converter.

a natural bidirectional input-series-output-parallel llc ...pe.csu.edu.cn/lunwen/a natural...

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